Nonlinear materials give rise to a multitude of optical phenomena that have important applications in technology and fundamental science. One example is wave mixing, in which light of two different frequencies can be added or subtracted through nonlinear optical responses to create light at new frequencies. Wave mixing is an important optical process since it is able to generate light at frequencies that are not available in typical lasers and/or frequencies for which efficient photodetectors are available. Another example is optical bistability, in which the intensity of output light can take two distinct stable values for a given input, creating an optical two-state system. Bistable devices, such as optical logic gates and memory, are important for optical computing, which has the potential for much faster computation speeds than those in current computation devices. Yet another example is self-focusing, in which a light pulse through an optical fiber with suitable nonlinearity can maintain its shape when propagating a long distance in the fiber. Self-focusing is important for long-distance telecommunications.
The degree of optical nonlinearity in a material depends upon the strength of the optical field, and varies across different materials. For a nonlinear material of the Kerr-type, the relative permittivity, ∈, is dependent upon the electric field, E, as expressed by ∈(E)=∈l+χ(3)|E|2, where ∈l is the linear relative permittivity of the material and χ(3) is the third-order nonlinear coefficient of the material. The nonlinear contribution to optical processes becomes significant when χ(3)|E|2 is of the order of ∈l, which is generally realized with a relatively strong electric field, as the third-order nonlinear coefficient is relatively small in naturally occurring optical materials. Accordingly, intense laser light is typically needed to observer nonlinear optical phenomena, limiting the application of nonlinear optics.
At least some nonlinear optical components utilize nonlinear resonators for switching and modulation. However, a modulation speed and an available fractional bandwidth of known high quality-factor (high-Q) nonlinear resonators are reduced by the relatively large Q values.
For at least some known imaging applications, the diffraction limit restricts the resolution of conventional microscopy to no less than half an operating wavelength, as evanescent waves that carry subwavelength information decay exponentially. By measuring an evanescent field directly, near-field scanning optical microscopy (NSOM) exhibits a high resolution beyond the diffraction limit. The resolution of NSOM, which depends on the size of the aperture regardless of the operating wavelength, has been demonstrated down to 20 nanometers (nm). However, for an aperture with size r in an infinitely thin film made of perfect metal, the transmitted power is proportional to (r/λ)4, where λ is the wavelength of the normal incident light. For a relatively small aperture in a metal with finite thickness and conductance the transmitted power is even weaker.
To enhance the transmitted power, various possible designs with a single aperture have been proposed, ranging from periodic corrugations to the C-shape apertures, which have been shown to enhance the transmission efficiency by two to three orders of magnitude. Further, subwavelength periodic apertures have been demonstrated to achieve improved transmission for potential applications for near field microscopy. However, at least some known strongly coupled periodic apertures exist in such a configuration that each measurement contains the information from all the apertures. Therefore, decomposing the coupled measurements to reconstruct an image may be relatively difficult.